Reading Diary: Birth of a Theorem: A Mathematical Adventure by Cédric Villani

Cédric Villani's Birth of a Theorem: A Mathematical Adventure has risen to the top of my Best Science Book of 2015 list. It'll be tough for another book to kick it off that summit before the end of the year, that's for sure.

The name Cédric Villani probably sounds a bit familiar to most who follow the science world reasonably closely. That's because he's the spider-pendant wearing, cravat and three-piece suit porting, Fields Medal winning French mathematician who's currently the director of the Institut Henri Poincaré in Paris. He's known in math circles for his work on nonlinear Landau damping with Clément Mouhot.

Birth of a Theorem is his memoir of how he and Mouhot made their breakthrough in nonlinear Landau damping. Curiously, the book really isn't about nonlinear Landau damping itself, barely including any kind of non-specialist description of it all all. Rather BoaT is about how they made their discoveries. It's about process, not product.

So the book includes copious email discussions between the two, some barely comprehensible to non-specialists, including TeX code and equations. It includes digressions and discussions, explanations of illuminations about the famous figures in their field, side trips into the music Villani likes to listen to while working. It's about the importance of collaborators and mentors in the scientific enterprise. It's about needing time to think deeply, away from pedestrian concerns, to get to the heart of the math. The serendipity and randomness of learning new things and making unexpected connections. It's about the challenge of finding good bread and cheese in New Jersey.

And lots and lots of rumination about work/life balance, juggling spending time with his small children, balancing his wife's career and his own, and the challenges of relocating to Princeton and the Institute for Advanced Study for six months and throwing all those balls up into the air, working in the shadow of Einstein. Mostly it's about balancing total immersion into the world of pure math with the demands of the very real and impure world of people and institutional politics and collaborators and family and life and death. Is Villani rather self-absorbed? Do we feel for his poor wife and kids at times? Sure, but we also root for him fiercely, hoping that he and Mouhot will slay their dragon.

And as incomprehensible as some of the math is, the process is vibrant and alive like in few other books I've read. Something like Wrinkles in Time: Witness to the Birth of the Universe by George Smoot and Keay Davidson comes to mind as a similar example from what I've read before.

I would recommend this book without hesitation. Malcolm DeBevoise's translation is smooth and seamless. BoaT would make a great gift to any science- or math- loving member of your extended circle. In particular, for anyone contemplating a research career, this book would provide an amazing insight into how research actually happens, especially in the more abstract areas of math and science. This book should find an eager audience for any library that collects popular science.

In many ways, Villani has only whetted my appetite for learning about the processes of mathematical discovery. Michael Harris's Mathematics without Apologies: Portrait of a Problematic Vocation seems like an interesting second step in this adventure. It's much longer and from the reviews and descriptive material, it looks like it just might pick up from where Villani left off, taking us from the unraveling of one discovery into a more generalized discussion of how the mathematical mindset works.

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